One night at McDonald's, the fry cook asked the cashier "How old are those three customers?"

"Well," replied the cashier, "the product of their ages is 16170 and the sum of their ages is three times your age."

"I'm afraid I still don't know" said the fry cook.

"Ah, none of them are the same age as you! You should be able to figure out their ages now!" cried the cashier.

“Why thank you!” said the fry cook, ”Now I know their ages!”

What is the positive difference between the age of the oldest customer and the youngest customer?

[This question is correctly phrased. There is enough information to arrive at a unique answer.]

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